Quantum dots can be called boxes of quantized potential on the hyperfine scale in which carriers (conduction electrons and holes) are confined in three dimensions. The density of the state function of carriers in a quantum dot is broken up according to a delta function, and the injected carriers are concentrated in these discrete energy levels. As a result, light which is emitted when the conduction electrons and holes recombine in the interior of quantum dots is of high optical intensity, and moreover, the width of the spectrum is extremely narrow.
In a semiconductor laser in which quantum dots having these properties are provided in an active layer, the reduced threshold current which is required for laser oscillation and the decrease in carriers results in reduced internal loss, and therefore, improved oscillation efficiency. In addition, the marked change in gain peak with respect to change in the carrier density enables high-speed operation. (A semiconductor laser in which quantum dots are applied in the active layer is hereinbelow referred to as a “quantum dot laser.”)
The realization of a quantum dot laser having these superior properties requires that quantum dots be formed at high density and with high uniformity, and moreover, without degrading crystallinity. Methods that are known from the prior art for forming such quantum dots include methods which employ such techniques as lithography and dry etching. However, these methods have the drawback that processing damage which occurs in the semiconductor crystal as a result of lithography or dry etching greatly reduces the light emission efficiency.
As a method of eliminating this problem, a “Direct formation method (or Self-organizing method)” has been developed and put into actual use in recent years. In this method, quantum dots are formed merely by growing crystals.
The direct formation method was reported by D. Leonard et al. in 1993. This method was proposed based on the finding that when a lattice-misfit InGaAs is grown on a GaAs substrate, the InGaAs grows as a layer until it exceeds a critical film thickness, and upon exceeding the critical film thickness, grows as islands, these island InGaAs crystals having a size of several tens of nanometers. This size is suitable for quantum dots [D. Leonard et al., Applied Physics Letters, Vol. 63, No. 23, pp. 3203-3205, December 1993]. The direct formation method was subsequently confirmed to be an excellent method for forming quantum dots.
The application of quantum dots formed by the direct formation method to semiconductor lasers is currently being widely studied. For example, G. T. Liu et al. have demonstrated that a quantum dot laser fabricated using the direct formation method operates with a lower injected current density than a prior-art semiconductor laser having an active layer of a bulk structure or quantum well structure [G. T. Liu et al., Electronics Letters, Vol. 35, No. 14, pp. 1163-1165, Jul. 8, 1999].
Further, Chen has demonstrated that the operating current of a quantum dot laser which has been fabricated using the direct formation method is not influenced by temperature [H. Chen et al., Electronics Letters, Vol. 36, No. 20, pp. 1703-1704, Sep. 28, 2000].
However, a quantum dot laser which has an operating speed surpassing that of a semiconductor laser of the prior art having an active layer of bulk structure or quantum well structure has not yet been proposed. This is due to problems described hereinbelow that are inherent to quantum dots.
According to the Pauli exclusion principal, only two conduction electrons and two holes can exist in each of the lowest energy levels (ground levels) of the conduction band and valence band in a quantum dot which has been quantized in three dimensions. As a result, if the ground levels of the conduction band and valence band are already occupied by conduction electrons and holes (carriers), additional conduction electrons or holes cannot be injected in the ground level. The transition of conduction electrons and holes from excited levels to the ground levels of the conduction band and valence band is referred to as “relaxation.”
Accordingly, in a quantum dot laser which is oscillated by the injection of a multiplicity of carriers into a plurality of quantum dots formed in an active layer, the relaxation rate of electrons which transition from excited levels of the conduction band (an energy level which is higher than the ground level of the conduction band) to the ground level steadily drops with increase in the number of injected conduction electrons. On the other hand, the relaxation rate of holes which transition from an excited level of the valence band (an energy level which is lower than the ground level of the valence band) to the ground level drops steadily with increase in the number of holes that are injected.
FIG. 1 is a graph showing the emission (photoluminescence, PL) spectrum of a semiconductor sample in which a plurality of InAs quantum dots are formed on a GaAs substrate. The emission spectrum shown in FIG. 1 shows the results of measuring light which is emitted when excitation light is irradiated onto the sample to cause the generation of carriers inside the sample and the recombination of these generated carriers inside the InAs quantum dots. In addition, FIG. 2 is a graph showing the relation between the excitation power and the ratio (I2/I1) of emission intensity I1 from the ground level to emission intensity I2 from the excited level of the quantum dots for the sample that produced the emission spectrum of FIG. 1.
As can be understood from FIG. 1 and FIG. 2, as the excitation power increases, emission intensity I1 from the ground level first increases and gradually approaches saturation, following which emission intensity I2 from the excited level increases. The excited level emission intensity I2 begins to gradually increase before the emission intensity I1 from the ground level reaches complete saturation.
Here, if the thermal excitation of carriers to excited levels is considered, the change over time in the number of carriers at an excited level can be given by the following equation (1):
                                          ∂                          N              1                                            ∂            t                          =                                            N              2                                      τ                              r                ⁢                                                                  ⁢                2                                              -                                    N              1                                      τ                              r                ⁢                                                                  ⁢                2                                              -                                    N              1                                                      τ                                  2                  -                  1                                                            exp                ⁡                                  (                                      -                                                                  Δ                        ⁢                                                                                                  ⁢                                                  E                                                      2                            -                            1                                                                                              kT                                                        )                                                                                        (        1        )            
In equation (1), N1 and N2 represent the number of carriers at the ground level and excited level, respectively; τr1 and τr2 represent the radiative recombination times of the ground level and excited level, respectively; τ2-1 is the relaxation time of carriers from the excited level to the ground level; ΔE2-1 represents the energy difference between the excited level and the ground level; k is the Boltzmann constant; and T is the absolute temperature.
In a stationary state, the left side of equation (1) is “0” and the ratio (I2/I1) of excited level emission intensity I2 to ground level emission intensity I1 can therefore be shown by equation (2) below:
                                          I            2                                I            1                          =                                                            N                2                                            τ                                  r                  ⁢                                                                          ⁢                  2                                                                                    N                1                                            τ                                  r                  ⁢                                                                          ⁢                  1                                                              =                                                    τ                                  2                  -                  1                                            +                                                τ                                      r                    ⁢                                                                                  ⁢                    1                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                        Δ                          ⁢                                                                                                          ⁢                                                      E                                                          2                              -                              1                                                                                                      kT                                                              )                                                                                      τ                              r                ⁢                                                                  ⁢                2                                                                        (        2        )            
As can be understood from equation (2), emission intensity ratio (I2/I1) is a function of the absolute temperature T.
In the above-described semiconductor sample (in which InAs quantum dots are formed on a GaAs substrate), if ΔE2-1 is assumed to be 73 meV, τr1 to be 0.7 ns and τr2 to be 0.5 ns at room temperature (293 K), the relation of the excitation power to relaxation time τ2-1 of carriers, which is found from the change in the emission intensity ratio (I2/I1) shown in FIG. 2 is as shown in FIG. 3.
As can be understood from FIG. 3, as the excitation power increases, the relaxation time τ2-1 of the carriers gradually increases due to filling of carriers at the ground level and thus approaches the radiative recombination times τr1 and τr2 (approximately 1 ns) of the ground level and excited level.
Thus, when the excitation power is 100 W/cm2,i.e., when the same carrier density can be obtained as during laser oscillation, the carrier relaxation time τ2-1 becomes 0.2 ns at room temperature (293 K). In this case, the 3-dB modulation bandwidth f3dB given by the following equation (3) is 0.8 GHz. In other words, the 3-dB modulation band f3dB, which is the frequency range in which direct modulation is possible, is limited to 0.8 GHz.
                              f                      3            ⁢            dB                          =                  1                      2            ⁢                          πτ                              2                -                1                                                                        (        3        )            
As is obvious from the foregoing explanation, the modulation rate in a quantum dot device such as a quantum dot laser drops due to decrease in the relaxation rate of carriers (increase in carrier relaxation time τ2-1), and this limited modulation rate complicates the realization of a modulation bandwidth on the order of 10 GHz, which is required in a current optical communication system.
The present invention was developed to overcome the above-described problems inherent to the prior art and has as an object the provision of a quantum dot device which, by accelerating the relaxation of carriers to the ground level in quantum dots, can realize a broad modulation band of at least approximately 10 GHz and high-speed operation.